Question

Which of these choices show a pair of equivalent expressions? CHECK ALL THAT APPLY

Answer 1

Answer:

Option C & D

Step-by-step explanation:

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FACTS TO KNOW BEFORE SOLVING :-

Lets say there's an expression $x^{\frac{a}{b} }$ .

It can be also written it as → $(\sqrt[b]{x} )^{a}$ and vice-versa.

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Lets come to the question.

• In option A , $7^{\frac{5}{7} }$ can be also written as $(\sqrt[7]{7} )^{5}$ . But it doesn't match with the other expression given. Hence they are not equivalent expressions.

• In option B , $6^{\frac{2}{7} }$ can be also written as $(\sqrt[7]{6} )^{2}$ . But it doesn't match with the other expression given. Hence they are not equivalent expressions.

• In option C , $5^{\frac{3}{2} }$ can be also written as $(\sqrt{5} )^{3}$. Hence they are equivalent expressions.

• In option D , $(\sqrt[4]{81} )^{5}$ can be also written as $81^{\frac{5}{4} }$ . Hence they are equivalent expressions

Thus , Option C & D are correct.